Loading...
Search
Toggle navigation
JCM
Home
About Journal
Information for Authors
Editorial Board
Subscription
Editorial Office
Table of Content
15 September 2020, Volume 38 Issue 5
Previous Issue
Next Issue
A MULTIDIMENSIONAL FILTER SQP ALGORITHM FOR NONLINEAR PROGRAMMING
Wenjuan Xue, Weiai Liu
2020, 38(5): 683704. DOI:
10.4208/jcm.1903m20180072
Asbtract
(
13
)
PDF
(305KB) (
27
)
References

Related Articles

Metrics
We propose a multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al.[SIAM J. Optim., 2005] is extended to solve constrained optimization problems. In our proposed algorithm, the constraints are partitioned into several parts, and the entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but the individual behavior of each part of constraints is considered. One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears. The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used. We prove that our algorithm is globally convergent to KKT points under the constant positive generators (CPG) condition which is weaker than the wellknown MangasarianFromovitz constraint qualification (MFCQ) and the constant positive linear dependence (CPLD). Numerical results are presented to show the efficiency of the algorithm.
ON ENERGY CONSERVATION BY TRIGONOMETRIC INTEGRATORS IN THE LINEAR CASE WITH APPLICATION TO WAVE EQUATIONS
Ludwig Gauckler
2020, 38(5): 705714. DOI:
10.4208/jcm.1903m20180090
Asbtract
(
12
)
PDF
(145KB) (
10
)
References

Related Articles

Metrics
Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered. Under a condition of Hairer & Lubich on the filter functions in the method, a modified energy is derived that is exactly preserved by trigonometric integrators. This implies and extends a known result on alltime nearconservation of energy. The extension can be applied to linear wave equations.
DEVELOPABLE SURFACE PATCHES BOUNDED BY NURBS CURVES
Leonardo Fern, ezJambrina, Francisco P, erezArribas
2020, 38(5): 715731. DOI:
10.4208/jcm.1904m20180209
Asbtract
(
19
)
PDF
(1460KB) (
19
)
References

Related Articles

Metrics
In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary curves. The reparameterization function is the solution of an algebraic equation. For the relevant case of cubic or cubic spline curves, this equation is quartic at most, quadratic if the curves are B′ezier or splines and lie on parallel planes, and hence it may be solved either by standard analytical or numerical methods.
CORNERCUTTING SUBDIVISION SURFACES OF GENERAL DEGREES WITH PARAMETERS
Yufeng Tian, Maodong Pan
2020, 38(5): 732747. DOI:
10.4208/jcm.1905m20180274
Asbtract
(
10
)
PDF
(6626KB) (
12
)
References

Related Articles

Metrics
As a cornercutting subdivision scheme, LaneRiesefeld algorithm possesses the concise and unified form for generating uniform Bspline curves:vertex splitting plus repeated midpoint averaging. In this paper, we modify the second midpoint averaging step of the LaneRiesefeld algorithm by introducing a parameter which controls the size of corner cutting, and generalize the strategy to arbitrary topological surfaces of general degree. By adjusting the free parameter, the proposed method can generate subdivision surfaces with flexible shapes. Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other stateoftheart approaches by carefully choosing the free parameters.
CONVERGENCE AND OPTIMALITY OF ADAPTIVE MIXED METHODS FOR POISSON'S EQUATION IN THE FEEC FRAMEWORK
Michael Holst, Yuwen Li, Adam Mihalik, Ryan Szypowski
2020, 38(5): 748767. DOI:
10.4208/jcm.1905m20180265
Asbtract
(
10
)
PDF
(411KB) (
5
)
References

Related Articles

Metrics
Finite Element Exterior Calculus (FEEC) was developed by Arnold, Falk, Winther and others over the last decade to exploit the observation that mixed variational problems can be posed on a Hilbert complex, and Galerkintype mixed methods can then be obtained by solving finitedimensional subcomplex problems. Chen, Holst, and Xu (Math. Comp. 78 (2009) 3553) established convergence and optimality of an adaptive mixed finite element method using RaviartThomas or BrezziDouglasMarini elements for Poissonls equation on contractible domains in ${\Bbb R}$
^{2}
, which can be viewed as a boundary problem on the de Rham complex. Recently Demlow and Hirani (Found. Math. Comput. 14 (2014) 13371371) developed fundamental tools for a posteriori analysis on the de Rham complex. In this paper, we use tools in FEEC to construct convergence and complexity results on domains with general topology and spatial dimension. In particular, we construct a reliable and efficient error estimator and a sharper quasiorthogonality result using a novel technique. Without marking for data oscillation, our adaptive method is a contraction with respect to a total error incorporating the error estimator and data oscillation.
TWOSTAGE FOURTHORDER ACCURATE TIME DISCRETIZATIONS FOR 1D AND 2D SPECIAL RELATIVISTIC HYDRODYNAMICS
Yuhuan Yuan, Huazhong Tang
2020, 38(5): 768796. DOI:
10.4208/jcm.1905m20180020
Asbtract
(
8
)
PDF
(2707KB) (
4
)
References

Related Articles

Metrics
This paper studies the twostage fourthorder accurate time discretization[J.Q. Li and Z.F. Du, SIAM J. Sci. Comput., 38 (2016)] and its application to the special relativistic hydrodynamical equations. Our analysis reveals that the new twostage fourthorder accurate time discretizations can be proposed. With the aid of the direct Eulerian GRP (generalized Riemann problem) methods and the analytical resolution of the local "quasi 1D" GRP, the twostage fourthorder accurate time discretizations are successfully implemented for the 1D and 2D special relativistic hydrodynamical equations. Several numerical experiments demonstrate the performance and accuracy as well as robustness of our schemes.
ACCURATE AND EFFICIENT IMAGE RECONSTRUCTION FROM MULTIPLE MEASUREMENTS OF FOURIER SAMPLES
T. Scarnati, Anne Gelb
2020, 38(5): 797826. DOI:
10.4208/jcm.2002m20190192
Asbtract
(
31
)
PDF
(2220KB) (
57
)
References

Related Articles

Metrics
Several problems in imaging acquire multiple measurement vectors (MMVs) of Fourier samples for the same underlying scene. Image recovery techniques from MMVs aim to exploit the joint sparsity across the measurements in the sparse domain. This is typically accomplished by extending the use of
l
_{1}
regularization of the sparse domain in the single measurement vector (SMV) case to using
l
_{2,1}
regularization so that the "jointness" can be accounted for. Although effective, the approach is inherently coupled and therefore computationally inefficient. The method also does not consider current approaches in the SMV case that use spatially varying weighted
l
_{1}
regularization term. The recently introduced variance based joint sparsity (VBJS) recovery method uses the variance across the measurements in the sparse domain to produce a weighted MMV method that is more accurate and more efficient than the standard
l
_{2,1}
approach. The efficiency is due to the decoupling of the measurement vectors, with the increased accuracy resulting from the spatially varying weight. Motivated by these results, this paper introduces a new technique to even further reduce computational cost by eliminating the requirement to first approximate the underlying image in order to construct the weights. Eliminating this preprocessing step moreover reduces the amount of information lost from the data, so that our method is more accurate. Numerical examples provided in the paper verify these benefits.
Current Issue
Earlier Issues
Advanced Search
Most Read Articles
Most Downloaded Articles
Visit Hong Kong Site